The generator matrix

 1  0  1  1  1 X^3+X^2+X  X  1  1 X^3+X^2  1  1  1  1  1  1 X^3 X^2+X  1 X^3+X  1  X  1  1  1  1  X X^3
 0  1 X+1 X^2+X X^3+X^2+1  1  1 X^3 X^2+1  1 X^2+X+1 X^3+X^2+X X^3+1 X^3+X X+1 X^2+1  1  1  1  1 X^3+X^2  1  X  X X^2 X^3+X^2+X  X  X
 0  0 X^2  0 X^3+X^2 X^2 X^3+X^2 X^2 X^3  0 X^3+X^2 X^2 X^3  0 X^3 X^3 X^2  0 X^2  0  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2
 0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0
 0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3

generates a code of length 28 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+133x^24+192x^25+640x^26+512x^27+1053x^28+704x^29+592x^30+128x^31+114x^32+16x^34+7x^36+4x^40

The gray image is a linear code over GF(2) with n=224, k=12 and d=96.
This code was found by Heurico 1.16 in 0.093 seconds.